Question

carla can choose two of her three pairs of sneakers to take to a track meet. if the pairs of sneakers are called a, b, and c, which choice represents the sample space, s, for the event?
○ s = {abc}
○ s = {abc, cab}
○ s = {ab, ac, bc}
○ s = {ab, ba, ac, ca, bc, cb}

Explanation:

Step1: Understand Sample Space for Combinations

When choosing 2 out of 3 pairs (A, B, C) without regard to order (since choosing AB is the same as BA for taking two pairs), we use combinations. The possible pairs are formed by selecting 2 distinct elements from the set {A, B, C}.

Step2: List All Possible Combinations

• Pair 1: A and B (represented as AB)
• Pair 2: A and C (represented as AC)
• Pair 3: B and C (represented as BC)

So the sample space \( S \) should contain these three combinations.

Answer:

\( S = \{AB, AC, BC\} \) (the third option)